Sawtooth cycle revisited

Abstract

Solving the pressure Poisson equation dominates a large portion of computational time for incompressible fluid flow simulations. To solve the pressure Poisson equation efficiently, geometric multigrid methods are used directly or used as the preconditioner for the conjugate gradient (CG) method. Conventionally, the V-cycle multigrid method is widely employed, and little attentionhas been paid to other cycles. In this paper, we introduce the sawtooth cycle multigrid method and its simple extension called N-cycle, which provides better convergence in equal time comparison with the V-cycle as a direct solver of the pressure Poisson equation. We also apply the N-cycle to the preconditioner of the CG method and show that the N-cycle multigrid CG method can provide better convergence than the V-cycle multigrid CG method.